Pochhammer-Chree Waves: Spectral Analysis of Axially Symmetric Modes

Abstract

The exact solutions of the linear Pochhammer-Chree equation for propagating harmonic waves in a cylindrical rod, are analyzed. Limiting velocities of the Pochhammer-Chree waves are discussed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes of the Pochhammer-Chree waves is performed. Analytical expressions for displacement fields are derived.